Advances in Difference Equations
Volume 2011 (2011), Article ID 357580, 9 pages
doi:10.1155/2011/357580
Research Article

Fractional-Order Variational Calculus with Generalized Boundary Conditions

Mohamed A. E. Herzallah1,2 and Dumitru Baleanu3,4

1Faculty of Science, Zagazig University, Zagazig, Egypt
2Faculty of Science in Zulfi, Majmaah University, Zulfi 11932, P.O. Box 1712, Saudi Arabia
3Department of Mathematics and Computer Science, Çankaya University, 06530 Ankara, Turkey
4Institute for Space Sciences, P.O.Box MG-23 Magurele, 76900 Bucharest, Romania

Received 18 September 2010; Accepted 8 November 2010

Academic Editor: J. J. Trujillo

Copyright © 2011 Mohamed A. E. Herzallah and Dumitru Baleanu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents the necessary and sufficient optimality conditions for fractional variational problems involving the right and the left fractional integrals and fractional derivatives defined in the sense of Riemman-Liouville with a Lagrangian depending on the free end-points. To illustrate our approach, two examples are discussed in detail.